If the radius of a sphere is increased by 50%, by what percent its volume will…

Let the original radius be r.

When the radius is increased by 50%, the new radius becomes:

New radius = 1.5r

Since volume varies as the cube of the radius,

New Volume : Original Volume

= (1.5r)³ : r³

= 1.5³

= 3.375

Thus, the new volume is 3.375 times the original volume.

Percentage increase in volume

= (3.375 − 1) × 100

= 2.375 × 100

= 237.5%

Therefore, the volume increases by 237.5%.

Answer: C) 237.5%